"Do I know how I feel? Do I know what I think? / Let me take ink and paper, let me take pen and ink." The young TS Eliot, in an untitled poem not published till Christopher Ricks's edition of Inventions of the March Hare in 1996, is urgently engaged in writing to find out exactly how he thinks and feels, and to find true expression for his temperament. He doesn't, however, do so to his own satisfaction, for he goes on: "There is something which should be firm but slips, just at my finger tips."

Authentic utterance is still only on the tip of his tongue, or rather on that of his pen. In other words he has yet, in Helen Vendler's phrase, to "come of age as a poet", is still serving his arduous apprenticeship. It is with "The Love Song of J Alfred Prufrock" that he crosses that threshold, Vendler claims, as Milton does with "L'Allegro", Keats with "On First Looking into Chapman's Homer" and Plath with "The Colossus". Vendler's splendid new book, with its title's echo of Margaret Mead's Coming of Age in Samoa , is, one might say, an exercise in literary anthropology, a clear but subtle account of the struggles, the rites of passage, undergone by four poets, while still in their 20s, negotiating with tradition in order to find their style and attain their majority - to become, in fact, major poets.

Her donnée is deceptively simple: she sets herself to write in depth about "the first 'perfect' poem each of these poets writes". Each chapter becomes a short story, a thrillingly compressed account of the vicissitudes of genius, focused on and leading up to (and in some cases looking ahead from) the selected work. Her word "perfect" will raise some eyebrows, but is carefully qualified: "I call such poems 'perfect' because they manifest a coherent and well-managed idiosyncratic style voiced in memorable lines; one would not wish them other than they are."

In these breakthrough poems Milton becomes Miltonic, Keats Keatsian: elements that have previously been unstable in the poet's work - in what become the juvenilia - reach a satisfactory balance or relationship for the first time.

Such a hitting of stride is a reward for much hard work, the result of "the private, intense, and ultimately heroic effort and endurance that precede the creation of any memorable poem".

If this sounds rather familiar in outline - for instance Lawrence Lipking's fine The Life of the Poet: Beginning and Ending Poetic Careers (1981) begins with Keats's self-discovery in the same "Chapman's Homer" sonnet - the detail of analysis and argument is what makes it so engaging. For Vendler, a passionate lover of poetry and perhaps its foremost advocate in America, who has written at book-length on Yeats, Herbert, Stevens, Hopkins, Heaney, Keats's odes and Shakespeare's sonnets, is one of our great close readers and expounders. It is a pleasure to be guided by her into the poet's workshop - she is so good at making poetry matter, at opening up the interest of passages one had dully taken for granted, breaking the ice that has formed above lines the eye had skated over.

There is little jargon or mystification in her approach: she believes in appreciating the structures and textures of poetry in a sharable way, pointing out and connecting up the finer points of the poet's work with a maximum of lucidity. Explicability is one of her watchwords, even where a pose of lofty authority or a grand invocation of the poetic mysteries might be a temptation. Thus, in Plath's best work, some accumulation of effect is always taking place, contributing its silent pressure to the "mysterious" (but explicable) conclusiveness of the close.

In "The Colossus", Vendler's chief example, Plath represents her dead father as a shattered giant statue which a stranded daughter is hopelessly trying to reconstruct. Ted Hughes says the poem was based on "a dream, which at the time made a visionary impact on her", and that it was "a poem which she regarded, at the time, as a breakthrough". Vendler feels this too - "Suddenly, one is reading the person who became 'Plath' "- and immediately proceeds to the question "But what is it in the style that causes that feeling?" The poem's potent last two lines express the daughter's isolation:

No longer do I listen for the scrape of a keel On the blank stones of the landing.

Potent, "mysterious" - but explicable. Vendler points out for one thing that we've been prepared for this mutedness: 19 of the poem's 30 lines have ended on a weak syllable ("keel" is strong, "landing" weak). She notes, further, that the onomatopoeia of "scrape" makes us hear it even as the speaker declares she's stopped listening. Also that "blank stones" picks up from the accumulation of bafflingly blank stones throughout the poem (the Colossus's "great lips", "acres . . . of brow", "immense skull-plates" and "bald, white tumuli"). The making of such helpful connections is typical of Vendler's generously imaginative project.

Vendler is then not merely an acutely sensitive reader, the great majority of whose intuitions and interpretations carry conviction, but also an indefatigable tracker-down and analyst of the intricate combinations of quasi-subliminal effects that make great poetry come alive. Her antennae are attuned here to the difficult discoveries she sees the beginning poet as desperately needing to make in order to win through to what is too easily called self-expression: of "a governing stylistic decorum" (the poet's own - it can't just be inherited); of "a growing awareness of the problems attending accurate expression of inner moods and attitudes" (blurting things out doesn't guarantee sincerity); and of "the salient elements of the outer sense-world that speak to his idiosyncratic imagination" (city grime for Eliot, the natural world and the legendary past for Keats). She also emphasises "the intuitive technical discoveries made in the course of early experimentation": in managing sound, rhythm, syntax, and larger formal units like stanzas and sonnets. She is especially good, as in her book on Shakespeare's sonnets, at discerning the organising patterns and structures within poems, and picking up the incongruities and contradictions which she often shows to lie at their heart.

This delightfully economical book is not only about these poets' introduction to poetry, it constitutes in itself an ideal, highly approachable introduction to poetry for what she calls "the new reader" - and there are many readers for whom a close involvement with poetry will be a novelty. She refers to the general lack of "school training in poetry", and her patient readiness to explicate and share her pleasure should make up for some of that educational deficit in the students and others who are lucky enough to read her. Her book, on the other hand, while eschewing flashy speculation, does not skirt difficulty, and has something valuable to add to scholarly debate at almost every turn. It should also speak directly to the young poet; for the last sentence predicts that "As we see new authors coming of age as poets, we will find in them comparable learning, experiment, generic invention, and imaginative mastery."

For Vendler, that is, the tradition is not broken, and the appreciation of new poets is not just an academic job but a high duty, indeed a passion. The young poets themselves, it must be said, those taking ink and paper as they begin their own apprenticeships in experiment and exploration, may well quail on reading the job description here. For Coming of Age as a Poet vividly portrays the risks, dangers and "ultimately heroic" efforts that great poets have had to put themselves through before their style achieves the weight to win them a place in the literary canon.

· Philip Horne is reader in English literature at University College London.